Conventional medical X-ray imaging devices rely on absorption properties of materials to provide information about interior structure of imaged objects. Such absorption type of imaging assumes non refractive X-rays penetrating the object under study. The contrast is produced because of the differences in the absorption cross section. While generally good contrast between highly attenuating (e.g., hard) and weakly attenuating (e.g., soft) materials is observed, the differentiation between soft-tissue materials can be difficult because of a low relative contrast. For example, the low-contrast soft tissue materials including, but not limited to vessels, cartilages, lungs, and breast tissues provide poor contrast in comparison to highly attenuating bone structures. The problem of soft-tissue imaging is addressed by interferometric X-ray imaging devices, which utilize the wave nature of X-ray radiation. Such imaging interferometers focus on measuring the refraction characteristics manifested in the process of X-rays passing through the object of study. In addition to absorption images of the object under study, these imaging interferometric devices can provide differential phase contrast images and dark-field images. We will refer to differential phase contrast imaging technique as DPCI. Differential phase contrast images contain information of X-ray phase shift properties through the object of study, e.g., similar to absorption imaging providing complementary knowledge of material properties. In contrast, dark-field images provide information about the local scattering of the object.
As an electromagnetic wave, the x-ray can be characterized by its frequency, amplitude, and phase. When an x-ray, as an electromagnetic wave, penetrates a medium, its amplitude is attenuated and phase is shifted. The refraction properties of X-rays penetrating the matter can be described by the complex index of refractionn=1−δ+iβ, where the imaginary part β contributes to the attenuation of the amplitude and the real part δ (refraction index decrement) is responsible for the phase shift. While the interferometer type of imaging devices can measure both β and δ terms, the conventional ones can detect only β. It can be shown that δ (rad/cm units) is about 103 to 104 times larger than β (1/cm units). Thus, the real part δ of the complex index of refraction provides a potential for imaging soft-tissue materials with higher contrast.
To date, several phase contrast imaging (PCI) techniques have been explored: 1) the interferometer technique, 2) the diffraction-enhanced imaging (DEI) technique, and 3) the free-space propagation technique. However, there are various practical problems associated with all three techniques. In the case of crystal interferometers and diffractometers, high temporal coherence (e.g., a high degree of monochromaticity) is required, which, in result, limits the application to a synchrotron radiation or a well defined monochromatic radiation source. In addition to the synchrotron source requirement, the use of multi-hole collimator in DEI limits the achievable spatial resolution and increases the acquisition time. The free-space propagation technique is limited in efficiency because of a requirement of high spatial coherence, which only can be obtained from an X-ray source with a very small focal spot size, or large propagation distance.
In addition, grating based differential phase contrast interferometry based on Talbot-Lau principles has been actively explored within the last decade. Such grating based differential phase contrast interferometry imaging devices can use a standard broadband X-ray tube when used together with a partially absorbing grating G0 (source grating), which can generate partially coherent X-ray radiation, and then the refraction characteristics of a scanned object can be detected via interference pattern, which is generated by a phase grating G1 and modulated onto an imaging detector (e.g., digital radiographic (DR) detector) by a partially absorbing grating G2.
Image acquisition procedures in the techniques described above typically require a plurality of X-ray exposures. Unanimously, all techniques described above require some of the geometrical parameters to be altered at each X-ray exposure. For example, a grating based inteferometry system requires one of the three gratings being translated (or stepped) with respect to the rest of the system at each X-ray exposure. Such an acquisition technique is referred to as phase stepping. The direction of the stepping (or scan) is typically perpendicular to trenches of the grating. The phase stepping acquisition for a grating based inteferometry system results in three images: 1) transmittance T image, 2) differential phase φ image, and 3) dark-field DF image. The transmittance image represents a mean intensity measured by detector over a phase-stepping cycle. The differential phase image represents a gradient of X-ray phase shift occurred in the object in the direction of phase stepping (e.g., the direction of the grating's translation (e.g., the direction in which the G2 grating is stepped)). The dark-field image reproduces the intensity modulation observed during the phase stepping relative to the mean signal (or contribution of the scattering effects).
Information included in each of the respective images is significantly different from each other. As described above, the actual phase shift though the object, which is proportional to refraction index decrement δ, is of a particular interest since the actual phase shift though the object can provide better soft-tissue contrast. To obtain such phase shift information, the differential phase image can be integrated along the differential direction (e.g., perpendicular to grating trenches and along phase stepping direction). Integration can correspond to dividing by the frequency in the spectral domain, and therefore low frequencies can be significantly amplified. Noise present in the differential phase data will get amplified along the direction of integration, which can result in severe streak artifacts, for example, oriented in the direction of integration.
Published US patent application 2013/0156284A1, “Regularized phase retrieval in differential phase-contrast imaging”; published paper, “Non-linear regularized phase retrieval for unidirectional X-ray differential phase contrast radiography” (Optics Express, V. 19, #25, pp. 25545-58, 2011); and published international application WO2012080125A1, “A method and a system for image integration using constrained optimization for phase contrast imaging with an arrangement of gratings” describe processes for solving problems of streak artifacts by regularizing the integration process of the differential phase data. These sources describe the regularization in the direction perpendicular to direction of integration of the differential phase, namely, one-dimensional regularization. One shortcoming of the described prior art is that in respective processes of eliminating streak artifacts, the regularization can also cause detail to be loss in the recovered phase. Detail loss can be highlighted for structures (e.g., edges) that are aligned with the direction of scanning and/or edges severely impacted by noise. Further, another shortcoming of the described prior art is that they do not account for a noise associated with non-uniformity of the grating structures (e.g., mostly manifested by non-uniformities in phase grating G1 and absorption grating G2).
Thus, there remains a need for phase retrieval methods, which can suppress streak artifacts without suppressing edges and can handle the non-uniformity of the grating structures in the phase image recovery.